Many holders of payment cards (credit and/or debit cards) find to their inconvenience that they wish to carry several such cards at the same time, potentially leading to overcrowding of the limited space in the holders' wallets. Among other proposed solutions, it has been proposed (e.g., in U.S. Pat. No. 6,631,849, issued to Blossom) to alleviate this problem with payment cards that carry two or more magnetic stripes, where each of the magnetic stripes is used to access a respective payment card account. This same problem potentially exists with respect to proximity payment devices, of which one example is the “PayPass”® card distributed by MasterCard International Incorporated, the assignee hereof. However there has been to date little or no detailed consideration of how to configure a proximity payment device to allow the user to access more than one account with a single device.